{
  "id": "2101.08871",
  "version": "v1",
  "published": "2021-01-21T22:23:38.000Z",
  "updated": "2021-01-21T22:23:38.000Z",
  "title": "Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles",
  "authors": [
    "Andres Fernandez Herrero"
  ],
  "comment": "65 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe an explicit Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles on a curve. It is based on the notion of parabolic slope, as in Mehta and Seshadri. We aim to give a treatment that is sheaf-theoretic and self-contained. We also prove the existence of schematic Harder-Narasimhan stratifications, which follows from an analogue of Behrend's conjecture in this context. A comparison with previous $\\Theta$-stratification approaches is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-21T22:23:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14D23"
    ],
    "keywords": [
      "parabolic vector bundles",
      "moduli stack",
      "explicit harder-narasimhan stratification",
      "schematic harder-narasimhan stratifications",
      "parabolic slope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}